If you downloaded content from websites other than YouTube the source of that content does not have permission from the copyright owner so anyone who downloads from them is breaking the law. The content found on YouTube is being posted by the individuals who own the actual copyright to that material, Since the content is coming from an authorized source you can view/listen to it without fear of legal consequence.
Now that we covered 'why' you can legally download from YouTube we must look at the 'how'. Whenever an individual goes to YouTube their Internet browser will present the streaming video and audio content on the screen for you but since this content is 'streaming' you cannot store it on your computer without first converting it to another file format (This is where the free YouTube downloader comes into play). While watching streaming content on YouTube is convenient you will not be able to entertain yourself if your WiFi connection is lost.